Constructions of Mutually Unbiased Bases
量子物理
2023-11-27 v1 新兴技术
摘要
Two orthonormal bases B and B' of a d-dimensional complex inner-product space are called mutually unbiased if and only if |<b|b'>|^2=1/d holds for all b in B and b' in B'. The size of any set containing (pairwise) mutually unbiased bases of C^d cannot exceed d+1. If d is a power of a prime, then extremal sets containing d+1 mutually unbiased bases are known to exist. We give a simplified proof of this fact based on the estimation of exponential sums. We discuss conjectures and open problems concerning the maximal number of mutually unbiased bases for arbitrary dimensions.
引用
@article{arxiv.quant-ph/0309120,
title = {Constructions of Mutually Unbiased Bases},
author = {Andreas Klappenecker and Martin Roetteler},
journal= {arXiv preprint arXiv:quant-ph/0309120},
year = {2023}
}
备注
8 pages latex